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@Thalesdisciple Yeah I'm mostly calling myself out as stevenclontz.github.io/intro-to-topology/ is absent of this intuition. But I am wondering if we couldn't define clos-OMG wait I remember now that this is already a thing! en.m.wikipedia.org/wiki/Proximity_space Maybe I should rewrite my IBME notes for those axioms...
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@Thalesdisciple Actually, maybe I really should. It's incredibly hard to motivate the axioms of a topology, but since I don't think intro students need to care about non-completely regular spaces, I can use the proximity axioms which have intuitive reasons.